{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 统计学习的对象是数据\n",
    "- 统计学习方法包括模型的假设空间、模型选择的准则以及模型学习的算法，称其为统计学习方法的三要素，简称为模型、策略和算法\n",
    "- 实现统计学习方法的步骤：\n",
    "\n",
    "    （1） 得到一个有限的训练数据集合；\n",
    "    \n",
    "    （2） 确定学习模型的集合；\n",
    "    \n",
    "    （3） 确定模型选择的准则，即学习的策略；\n",
    "    \n",
    "    （4） 实现求解最优模型的算法，即学习的算法；\n",
    "    \n",
    "    （5） 通过学习方法选择最优模型；\n",
    "    \n",
    "    （6） 利用学习的最优模型对新数据进行预测或分析\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.2  监督学习\n",
    "\n",
    "**基本概念**\n",
    "\n",
    "1. 输入空间、特征空间和输出空间\n",
    "    \n",
    "    有时假设输入空间与特征空间为相同的空间，有时假设不同，将实例从输入空间映射到特征空间。模型实际上都是定义在特征空间上的\n",
    "\n",
    "    输入变量X与输出变量Y： 均为连续变量的问题称为回归问题；输出变量为有限个离散变量的预测问题称为分类问题；输入变量与输出变量均为变量序列的问题称为标注问题\n",
    "    \n",
    "### 1.3 三要素\n",
    "\n",
    "**1. 模型**\n",
    "\n",
    "模型就是所要学习的条件概率分布或决策函数\n",
    "\n",
    "**2.策略**\n",
    "\n",
    "即如何在假设空间中找到最优模型：使用损失函数或风险函数。损失函数度量模型一次预测的好坏，风险函数度量平均意义下模型预测的好坏\n",
    "\n",
    "常用的损失函数有：（1）0-1损失函数；（2）平方损失函数；（3）绝对损失函数；（4）对数损失函数或对数似然函数\n",
    "\n",
    "风险函数是损失函数的期望。\n",
    "\n",
    "- 经验风险最小化与结构风险最小化:经验风险最小化就是是风险函数最小，当样本容量很小时，可能会产生过拟合现象。\n",
    "- 结构风险最小化可以防止过拟合，它等价于正则化，结构风险在经验风险上加上了表示模型复杂度的正则化项。\n",
    "\n",
    "**3. 算法**\n",
    "\n",
    "选择了最优模型后，考虑用什么样的计算方法求解最优模型。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.4 模型评估与模型选择\n",
    "1. 训练误差与测试误差\n",
    "2. 过拟合与模型选择\n",
    "    \n",
    "    若只考虑减少误差就可能产生过拟合，模型选择的方法有正则化与交叉验证"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "目标函数$y=sin2{\\pi}x$, 加上一个正态分布的噪音干扰，用多项式去拟合"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 过拟合与模型选择\n",
    "\n",
    "\n",
    "import numpy as np\n",
    "import scipy as sp\n",
    "from scipy.optimize import leastsq\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 目标函数\n",
    "def real(x):\n",
    "    return np.sin(2*np.pi*x)\n",
    "\n",
    "#多项式\n",
    "def fit(p,x):\n",
    "    f = np.poly1d(p)   # p是列表，长度代表最高次幂-1  元素是每一项的系数\n",
    "    return f(x)\n",
    "# 差\n",
    "def res(p,x,y):\n",
    "    ret = fit(p,x)-y\n",
    "    return ret\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 在目标函数上找10个点进行拟合\n",
    "\n",
    "x = np.linspace(0,1,10)    # 0-1 范围内均匀取10个点\n",
    "x_points = np.linspace(0,1,1000)\n",
    "\n",
    "y_ = real(x)   # 对应的y点\n",
    "\n",
    "y = [np.random.normal(0,0.1) +y1 for y1 in y_]  # 加上正态分布的噪声,得到的点不完全与real重合，对这些点进行拟合\n",
    "\n",
    "def fitting(M=0):\n",
    "    p_init = np.random.rand(M+1) #随机初始化多项式参数，M为多项式的次数（实际是P-1次，这里加上1）\n",
    "    p_lsq = leastsq(res,p_init,args=(x,y))  # 最小二乘法求最小值\n",
    "    \n",
    "    print('Fitting Parameters',p_lsq[0])\n",
    "    \n",
    "    plt.plot(x_points, real(x_points), label='real')          # 目标函数\n",
    "    plt.plot(x_points, fit(p_lsq[0], x_points), label='fitted curve')  # 拟合函数\n",
    "    plt.plot(x, y, '*', label='noise')                        # 点\n",
    "    \n",
    "    plt.legend()\n",
    "    return p_lsq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting Parameters [0.05411206]\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# M=0\n",
    "p_lsq_0 = fitting(M=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting Parameters [-1.30815175  0.70818793]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# M=1\n",
    "p_lsq_1 = fitting(M=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting Parameters [ 2.23181266e+01 -3.32191380e+01  1.11358412e+01 -2.50729390e-02]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "# M=3\n",
    "p_lsq_3 = fitting(M=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting Parameters [ 1.36029161e+04 -6.29877685e+04  1.21867442e+05 -1.27791504e+05\n",
      "  7.87394459e+04 -2.88368302e+04  6.03362487e+03 -6.61152720e+02\n",
      "  3.39118268e+01  6.48549952e-02]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# M=9\n",
    "p_lsq_9 = fitting(M=9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 监督学习的任务就是学习一个模型，监督学习方法又可以分为生成方法和判别方法，学习到的模型分别称为生成模型和判别模型。\n",
    "    - 生成方法学习的模型表示了给定输入X产生输出Y的生成关系，典型的生成模型有：朴素贝叶斯法和隐马尔可夫模型。\n",
    "    - 判别方法关心的是对给定的输入X，应该预测什么样的输出Y，典型的判别模型包括k近邻法、感知机、决策树、逻辑斯谛回归模型、最大熵模型、支持向量机、提升方法和条件随机场等\n",
    "    \n",
    "总结：生成方法学习的是输入输出的关系，收敛速度更快。判别关系注重决策函数，直接面对预测，学习的准确率更高"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
